A novel polymorphism in the PTC gene allows easy identification of allelic loss in basal cell nevus syndrome lesions

Basal cell nevus syndrome (BCNS; also nevoid basal cell carcinoma syndrome [NBCCS]; Gorlin's syndrome) is an autosomal dominant syndrome characterized by multiple basal cell carcinomas, keratocysts, and developmental skeletal defects. Mutation of the human homologue of Drosophila patched (PTC) gene is considered to be the molecular defect in BCNS. PTC mutations have been observed in sporadic tumors including basal cell and ovarian carcinomas and medulloblastoma. The authors report a novel C/T polymorphism in the PTC gene. Forty-eight normal blood samples were screened for the presence of the polymorphism using direct radioactive and automated sequencing of polymerase chain reaction (PCR) products and restriction enzyme digestion. Results demonstrated 20 homozygous T (43%), 11 homozygous C (23%), and 17 heterozygous C/T (35%). The presence of this polymorphism has permitted us to directly detect allelic loss in BCNS, sporadic keratocysts, and basal cell carcinoma (BCC). Further, four BCNS keratocysts and two BCNS-BCC and three non-BCNS keratocysts showed allelic loss of complementary DNA from lesions when compared with their corresponding blood genomic DNA.

Characterisation of the human and mouse orthologues of the Drosophila ariadne gene

The specificity of the ubiquitin degradation system is regulated through interaction between individual ubiquitin-conjugating enzymes (E2s) and multiple ubiquitin-protein ligases (E3s). Here we describe the characterisation of a novel gene (ARIH1) that encodes the human homologue of Drosophila ariadne which interacts with the E2s, UbcH7 and UbcH8 and represents a component of an E3 complex. Three PACs (189N19, 142P17 and 179H7) were isolated that contain this gene. Using these PACs as probes, we mapped ARIH1 to human chromosome 15q24 by fluorescence in situ hybridisation (FISH). Sequencing of the ARIH1 PACs showed that the gene has 13 introns. In addition, we isolated two PACs (345D8 and 571P19) containing the mouse orthologue (Arih1) of ARIH1. The intron-exon structure of Arih1 was identical to ARIH1 and the proteins demonstrated a 98% identity at the amino acid level. Furthermore, comparison of Drosophila ariadne with ARIH1 indicates an identity at the amino acid level of 70% and introns at 3/7 identical sites. The high degree of homology demonstrated by the mouse and human orthologues of Drosophila ariadne indicates an important, conserved biological function, consistent with a putative role in ubiquitylation.

Expression of Interleukin-18, a Th1 cytokine, in human gastric mucosa is increased in Helicobacter pylori infection

Interleukin-18 (IL-18), a cytokine that promotes Th1 responses, is processed to the active mature protein by caspase-1. The effects of Helicobacter pylori infection on gastric IL-18 and caspase-1 were examined. In antral mucosa, IL-18 mRNA expression was greater (P<.01) in H. pylori-positive (n=40) than in H. pylori-negative patients (n=29) with normal mucosa. Inactive precursor (24 kDa) and mature (18 kDa) IL-18 were present in antral biopsy specimens from uninfected and infected subjects. In corpus mucosa, mature IL-18 and a 16-kDa protein, corresponding to inactive IL-18, were present. Active caspase-1 p20 subunit was detected in antral and corpus mucosa of infected and uninfected subjects. These data show that, although H. pylori infection is associated with increased antral IL-18 mRNA expression, mature IL-18 protein and active caspase-1 p20 are present in mucosa of both H. pylori-infected and -uninfected subjects. IL-18 may have an important role in promoting gastric Th1 responses in H. pylori infection.

Selecting patients for combined femorofemoral bypass grafting and iliac balloon angioplasty and stenting for bilateral iliac disease

PURPOSE

This study examines the selection of patients for combined femorofemoral bypass (FFB) grafting and iliac balloon angioplasty (IBA) and stenting for bilateral iliac occlusive disease (successively or simultaneously) and the correlation of the length and location of stenoses of the donor iliac artery to the success of FFB grafts.

METHODS

Forty-one patients with long iliac occlusion and significant contralateral iliac stenosis were treated with combined FFB grafting and IBA and stenting, which were performed simultaneously or percutaneously within 1 to 2 days before surgery. Stenting was performed for suboptimal IBAs. IBA/graft patency was evaluated by duplex scanning/ankle-brachial index at 1, 3, 6, and 12 months and every 12 months thereafter. A life-table analysis of patency was performed, according to the length of stenosis as classified by the Society of Cardiovascular Interventional Radiology (group A, < 3 cm and 3-5 cm; group B, > 5 cm).

RESULTS

Indications for surgery were limb salvage (22%), rest pain (44%), and claudication (34%). The mean follow-up time was 34.1 months. Perioperative complications were 7% for group A versus 62% for group B (P = .0007) with no perioperative deaths or amputations. Stenting was needed in 12 of 13 patients (92%) in group B versus four of 28 patients (14%) in group A (P < .0001) and in 11 of 12 external iliac artery lesions versus five of 29 common iliac artery lesions (P < .0001). The overall early success rate was 100% for group A and 62% for group B (P = .0028). The primary patency rates at 1, 2, and 3 years were 96%, 85%, and 85% for group A, respectively, and for group B were 46%, 46%, and 31%, respectively (P < .01). The secondary patency rates for group A at 1, 2, and 3 years were 100%, 96%, and 87%, respectively; and for group B were 62%, 54%, and 27%, respectively (P < .001). The overall primary and secondary patency rates for common iliac and external iliac artery lesions were similar (72% and 72% versus 67% and 75%, respectively). The overall limb salvage rates were 96% for group A and 85% for group B. Seven of 13 patients (54%) of group B, in contrast with 0 of 28 patients in group A, had to undergo a revision of the procedure within 30 days (P < .01).

CONCLUSION

Combined use of IBA and stenting and FFB grafting is effective and durable and can be performed simultaneously, if the donor iliac stenosis length is 5 cm or less. Percutaneous transluminal angioplasty/stenting of stenoses of 5 cm or more fail to support FFB grafting in most patients; therefore, their combination should be questioned.

Prediction of electroencephalographic spectra from neurophysiology

A recent neurophysical model of propagation of electrical waves in the cortex is extended to include a physiologically motivated subcortical feedback loop via the thalamus. The electroencephalographic spectrum when the system is driven by white noise is then calculated analytically in terms of physiological parameters, including the effects of filtering of signals by the cerebrospinal fluid, skull, and scalp. The spectral power at low frequencies is found to vary as f(-1) when awake and f(-3) when asleep, with a breakpoint to a steeper power-law tail at frequencies above about 20 Hz in both cases; the f(-1) range concurs with recent magnetoencephalographic observations of such a regime. Parameter sensitivities are explored, enabling a model with fewer free parameters to be proposed, and showing that spectra predicted for physiologically reasonable parameter values strongly resemble those observed in the laboratory. Alpha and beta peaks seen near 10 Hz and twice that frequency, respectively, in the relaxed wakeful state are generated via subcortical feedback in this model, thereby leading to predictions of their frequencies in terms of physiological parameters, and of correlations in their occurrence. Subcortical feedback is also predicted to be responsible for production of anticorrelated peaks in deep sleep states that correspond to the occurrence of theta rhythm at around half the alpha frequency and sleep spindles at 3/2 times the alpha frequency. An additional positively correlated waking peak near three times the alpha frequency is also predicted and tentatively observed, as are two new types of sleep spindle near 5/2 and 7/2 times the alpha frequency, and anticorrelated with alpha. These results provide a theoretical basis for the conventional division of EEG spectra into frequency bands, but imply that the exact bounds of these bands depend on the individual. Three types of potential instability are found: one at zero frequency, another in the theta band at around half the alpha frequency, and a third at the alpha frequency itself.

Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part I. Method

We present a formulation for wave propagation and scattering through stacked gratings comprising metallic and dielectric cylinders. By modeling a photonic crystal as a grating stack of this type, we thus formulate an efficient and accurate method for photonic crystal calculations that allows us to calculate reflection and transmission matrices. The stack may contain an arbitrary number of gratings, provided that each has a common period. The formulation uses a Green's function approach based on lattice sums to obtain the scattering matrices of each layer, and it couples these layers through recurrence relations. In a companion paper [J. Opt Soc. Am. A 17, 2177 (2000)] we discuss the numerical implementation of the method and give a comprehensive treatment of its conservation properties.

Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part II. Properties and implementation

A numerical implementation and generalized conservation properties of a formulation for calculating wave propagation through stacked gratings comprising metallic and dielectric cylinders are presented. The basic formulation of the method was given in a companion paper [J. Opt. Soc. Am. A. 17, 2165 (2000)]. Here, details of the numerical implementation of the method are discussed and are illustrated for the ensemble average of a strongly scattering structure with refractive index and radius disorder. Also presented are a comprehensive treatment of energy conservation and generalized phase relations, as well as reciprocity.

Frequency of postoperative carotid duplex surveillance and type of closure: results from a randomized trial

BACKGROUND/PURPOSE

In several nonrandomized studies investigators have reported on the value of postoperative carotid duplex surveillance (PCDS) with mixed results; however the type of closure was not analyzed in these studies. In this study we analyze the frequency and timing of postoperative carotid duplex ultrasound scanning according to the type of closure from a randomized carotid endarterectomy (CEA) trial comparing primary closure (PC) versus patching.

PATIENT POPULATION AND METHODS

We randomized 399 CEAs into 135 PCs, 134 polytetrafluoroethylene (PTFE) patch closures, and 130 vein patch closures (VPCs) with a mean follow-up of 47 months. PCDS was done at 1, 6, and 12 months and every year thereafter (a mean of 4.0 studies per artery). Kaplan-Meier analysis was used to estimate the rate of > or = 80% restenosis over time and the time frame of progression from < 50%, to 50%-79% and > or = 80% stenosis.

RESULTS

Restenoses of > or =80% developed in 24 (21%) arteries with PC and nine (4%) with patching. Kaplan-Meier estimate of freedom of > or = 80% restenosis at 1, 2, 3, 4, and 5 years was 92%, 83%, 80%, 76%, and 68% for PC, respectively, and 100%, 99%, 98%, 98%, and 91% for patching, respectively, (P <.01). Of 56 arteries with 20% to 50% restenosis, two of 28 patch closures and 10 of 28 PCs progressed to 50% to < 80% restenosis (P =.02); none of the patch closures and six of 28 PCs progressed to > or =80% (P =.03). In PCs, the median time to progression from <50% to 50%-79%, < 50% to > or =80%, and 50%-79% to > or = 80% was 42, 46, and 7 months, respectively. Of the 24 arteries with > or =80% restenosis in PC, 10 were symptomatic. Thus, assuming th symptomatic restenosis would have undergone duplex scan examinations regardless, there were 14 asymptomatic arteries (12%) that could have been detected only with PCDS (estimated cost, $139, 200), and those patients would have been candidates for redo CEA. Of the 9 arteries (3 PTFE closures and 6 VPCs) with > or =80% restenosis with patch closures, 6 asymptomatic (4 VPCs and 2 PTFE closures) arteries (3%) could have been detected with PCDS. In patients with normal duplex scan findings at the first 6 months, only four (2%) of 222 patched arteries (two asymptomatic) developed > or = 80% restenosis versus five (38%) of 13 in patients with abnormal duplex scan examination findings (P<.001).

CONCLUSIONS

PCDS is beneficial in patients with PC, but is less beneficial in patients with patch closure. PCDS examinations at 6 months and at 1- to 2-year intervals for several years after PC are adequate. For patients with patching, a 6-month postoperative duplex scan examination with normal results is adequate.

Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals

The effects of disorder in the geometry and refractive index on the transmittance of two-dimensional photonic crystals composed of dielectric circular cylinders are considered, including randomness of radii, positions of the cylinder centers, and thickness of each layer of the photonic crystal. The effects of combinations of different types of strong disorder are also considered. The localization and homogenization properties of disordered photonic crystals are investigated. Analytical expressions for the two-dimensional localization length in the form of integrals are presented for both polarizations. It is shown numerically that the slope of the exponential divergence of the localization length in two dimensions is proportional to the inverse of the square of randomness for strong disorder and proportional to the inverse of the randomness for weak disorder. The effective dielectric constants for both polarizations in the case of strong disorder are also found. The transition from localization to homogenization is discussed and the terms responsible for this transition are identified and investigated.

Carotid-subclavian bypass grafting with polytetrafluoroethylene grafts for symptomatic subclavian artery stenosis or occlusion: a 20-year experience

BACKGROUND AND PURPOSE

Since the advent of subclavian artery percutaneous transluminal angioplasty/stenting, several authorities advocate it as the treatment of choice for patients with subclavian artery disease, claiming results equal to or better than those of reconstructive vascular surgery. However, most of their quoted surgical series included patients who may have other brachiocephalic disease who were treated nonuniformly by means of various bypass grafts with different grafts in the same series (eg, Dacron, polytetrafluoroethylene [PTFE], or vein). In this study, we analyze the long-term results of a large series of carotid-subclavian bypass grafts for subclavian artery disease in which PTFE was uniformly used; the study can be used as a future reference to compare the results of subclavian artery percutaneous transluminal angioplasty/stenting.

PATIENT POPULATION AND METHODS

Fifty-one patients with symptomatic subclavian artery disease (40 occlusions and 11 stenoses) who were treated with carotid-subclavian bypass grafts (PTFE [Goretex]) during a 20-year period were analyzed. Graft patency was determined clinically and confirmed with Doppler scanning pressures and duplex ultrasound scanning. The cumulative patency, overall survival, and symptom-free survival rates were calculated with the life table method.

RESULTS

Indications for surgery were arm ischemia in 34 patients (67%), vertebrobasilar insufficiency (VBI) in 27 (53%), and symptomatic subclavian steal in 7 (14%). A combination of arm ischemia and VBI occurred in 17 (33%) of these patients. The mean follow-up was 7.7 years with a median of 7.0 years (range, 1-19 years). The 30-day morbidity rate was 6%, with no perioperative stroke or mortality. Immediate relief of symptoms was achieved in 100% of patients; however, four patients (8%) had late recurrent symptoms (three with VBI). The primary patency and secondary patency rates at 1, 3, 5, and 10 years were 100%, 98%, 96%, and 92% and 100%, 98%, 98%, and 95%, respectively. The symptom-free survival rates at 1, 3, 5, and 10 years were 100%, 96%, 82%, and 47%, respectively. The overall survival rates at 1, 3, 5, and 10 years were 100%, 98%, 86%, and 57%. The mean hospital stay was 3.5 days in the late 70s and 80s and 2.1 days in the 90s (P <. 001).

CONCLUSIONS

Carotid-subclavian bypass grafts with PTFE grafts for subclavian artery disease are safe, effective, and durable and should remain the procedure of choice, particularly in good-risk patients.

Fine mapping of 12 previously unassigned EST clones to individual YACs in the familial Alzheimer's disease (FAD) region of chromosome 14q24.3

We have constructed an approximately 4-Mb YAC contig spanning the microsatellite markers D14S1028-D14S61 on chromosome 14q24.3 using oligonucleotide primers to microsatellite markers, ESTs and the genes PSEN1, FOS, TGFB3 and UBE2L1. This contig consists of 44 ICI YACs and 5 megaCEPH YACs. The data reported here should aid the final construction of an integrated map of chromosome 14 and allow the identification and accurate mapping of additional novel ESTs within this region.

Genomic organization of the human ubiquitin-conjugating enzyme gene, UBE2L6 on chromosome 11q12

The human UBE2L6 gene encodes UbcH8(Kumar), a ubiquitin-conjugating enzyme (E2) highly simliar in primary structure to UbcH7 which is encoded by UBE2L3. Like UBC4 and UBC5 in yeast, these proteins demonstrate functional redundancy. Herein we report the intron/exon structure of UBE2L6. Comparison of the genomic organization of UBE2L6 with UBE2L3 demonstrates that these genes remain highly conserved at the genomic as well as at the protein level. We also describe the chromosomal localization of UBE2L6, which maps to chromosome 11q12.

Effort subclavian vein thrombosis: evolution of management

PURPOSE

To analyze changes in the management of effort subclavian vein thrombosis at our institution.

METHODS

Records of 23 patients with effort subclavian vein thrombosis treated over a 10-year period were analyzed to compare the results of conventional therapy (heparin/warfarin) used in the first half of this period to a multimodality treatment strategy (thrombolysis and other adjunctive treatment as indicated, e.g., first rib resection, angioplasty/stenting, and vein reconstruction). Diagnostic testing included duplex ultrasound and venography. All patients had at least 1-year follow-up.

RESULTS

Eight patients (7 men; mean age 34 years, range 15-54) had conventional treatment (group A) and 15 patients (14 men; mean age 36 years, range 17-55) had multimodality therapy (group B). Demographics and clinical characteristics were comparable for both groups. Initial thrombolysis was achieved in 14 (93%) group B patients; 10 received adjunctive treatment to relieve external compression or vein stenosis. Four patients had successful first or cervical rib resection and scalenectomy, and first rib resection followed by angioplasty/stenting was successful in 2. However, angioplasty and stenting alone failed in 2 patients, while venous reconstruction was successful in only 1 of 2 cases. Mean follow-up was 72 months in group A patients and 59 months in group B. One (13%) group A patient and 12 (80%) group B patients demonstrated total venous recanalization and symptom resolution (p = 0.003). Overall, clinical resolution (total and partial symptom relief) was achieved in 3 (38%) group A patients and 13 (87%) group B patients (p = 0.026).

CONCLUSIONS

Initial lytic therapy followed by adjunctive treatment to relieve external venous compression or venous stenosis is effective in treating patients with effort subclavian vein thrombosis.

Mechanisms of cortical electrical activity and emergence of gamma rhythm

A continuum model of the electrical activity of the cerebral cortex is described which predicts the occurrence of a resonance in the gamma range near 40 Hz. The emergence of this resonance is due to two refinements to a previous model, namely the inclusion of a modulation of synaptic strength due to finite reversal potentials, and use of parameters that better match physiological measurements. Analytical expressions for the fixed points of the system and for its linear dynamics are found in terms of average neuronal properties, and together explain the occurrence and modulation of the gamma-like resonance. The analytical results are confirmed by a numerical simulation.

Death from early colorectal cancer is predicted by the presence of transcripts of the REG gene family

An intrinsic component of colorectal carcinogenesis may be the capacity to activate regenerative responses simultaneously with inhibition of apoptosis. Since apoptosis is known to be inhibited in colorectal cancer, this study sought evidence for the activation of the REG family of genes which are considered to be activated during regeneration of intestinal mucosa. Transcripts for the REG gene were found in 53% of colorectal cancers and for the PAP gene in 60% of colorectal cancers, by RT-PCR. Using in situ hybridization, the REG transcripts were found to be present in the tumour cells themselves rather than inflammatory or stromal cells. There were no significant correlations between the expression of these two genes and tumour stage, age or sex of the patient population or tumour site. However, in patients with non-metastatic disease who underwent ostensibly curative surgery, the expression of REG alone and co-expression of REG with PAP had a highly significantly adverse effect on survival. These data provide support for the concept that, in some tumours, carcinogenesis involves a regenerative process which co-exists with apoptotic inhibition and may provide a valuable selective indicator of the need for adjuvant therapy in those patients with early-stage colorectal cancer whose disease is destined to recur after curative surgery.

Promoter analysis of the human ubiquitin-conjugating enzyme gene family UBE2L1-4, including UBE2L3 which encodes UbcH7

UbcH7 is a ubiquitin-conjugating enzyme mediating c-fos degradation, transcription factor NF-kappaB maturation, human papilloma virus-mediated p53 and Myc protein degradation, in vitro. Previously, we characterised a highly dispersed gene family, UBE2L1-UBE2L4, whose members could potentially encode different isoforms of the UbcH7 protein. UBE2L3, located at chromosome 22q11.2, is the only identified family member with introns and encodes a polypeptide sequence identical to that of UbcH7. Promoter characterisation of UBE2L1, UBE2L3 and UBE2L4 5'-upstream regions was performed to establish which are transcribed under normal physiological conditions and after heat shock. Promoter activity was observed only with the UBE2L3 construct, the minimal promoter lying within a region 100 bp upstream of the transcriptional start site. No evidence for the presence of UBE2L1 or UBE2L4 transcripts was observed in human or murine tissues and cell lines. These data strongly suggest that UBE2L1 and UBE2L4 are likely to encode pseudogenes. Sequencing revealed that the UBE2L3 promoter contained no TATA or CCAAT boxes. Protein:DNA interaction studies confirmed the presence of binding sites for the transcription factors AP2 and Sp1 in the UBE2L3 minimal promoter. Deletion of these binding sites indicated that these factors are crucial for transcription of this gene.

A synergistic effect of a daily supplement for 1 month of 200 mg magnesium plus 50 mg vitamin B6 for the relief of anxiety-related premenstrual symptoms: a randomized, double-blind, crossover study

To investigate single and combined effects of daily dietary supplementation with 50 mg of vitamin B6 and 200 mg magnesium (as MgO) for one cycle for the relief of mild premenstrual symptoms, a randomized, double-blind, placebo-controlled, crossover design was used. Forty-four women with an average age of 32 years took part in the study. Each woman was randomly assigned, according to a Latin square design, to take consecutively all four of the following treatments daily for one menstrual cycle: (1) 200 mg Mg, (2) 50 mg vitamin B6, (3) 200 mg Mg + 50 mg vitamin B6 and (4) placebo. Throughout the study, each volunteer kept a daily record of symptoms using a 5-point ordinal scale in a menstrual diary of 30 symptoms. Symptoms were grouped into six categories: anxiety, craving, depression, hydration, other, and total. Urinary magnesium output for 24 hours was estimated using the Mg/creatinine concentration ratio. ANOVA showed no overall difference between individual treatments, but predefined treatment comparisons using factorial contrasts in ANOVA showed a significant effect of 200 mg/day Mg + 50 mg/day vitamin B6 on reducing anxiety-related premenstrual symptoms (nervous tension, mood swings, irritability, or anxiety) (p = 0.040). Urinary Mg output was not affected by treatment. A small synergistic effect of a daily dietary supplementation with a combination of Mg + vitamin B6 in the reduction of mild premenstrual anxiety-related symptoms was demonstrated during treatment of 44 women for one menstrual cycle. In view of the modest effect found, further studies are needed before making general recommendations for the treatment of premenstrual symptoms. The study indicated that absorption from MgO was poor and daily supplementation for longer than 1 month is necessary for tissue repletion.

Vertebrate pseudogenes

Pseudogenes are commonly encountered during investigation of the genomes of a wide range of life forms. This review concentrates on vertebrate, and in particular mammalian, pseudogenes and describes their origin and subsequent evolution. Consideration is also given to pseudogenes that are transcribed and to the unusual group of genes that exist at the interface between functional genes and non-functional pseudogenes. As the sequences of different genomes are characterised, the recognition and interpretation of pseudogene sequences will become more important and have a greater impact in the field of molecular genetics.

No polymorphism in the tissue transglutaminase gene detected in coeliac disease patients

BACKGROUND

The autoantigen for the anti-endomysial antibody (AEA) found in coeliac disease has recently been reported to be the enzyme tissue transglutaminase (tTG). Polymorphisms in the gene for tTG would result in different enzymic isoforms being expressed. Certain isoforms may interact with gliadin to create antigenic neoepitopes, which could then generate an immune response in genetically predisposed individuals possessing major histocompatibility complex (MHC) class II DQ2.

METHODS

We have sequenced the coding region of tTG in coeliac patients and normal controls. Total RNA was extracted from mucosal biopsies from eight AEA-positive histologically proven coeliac disease patients and four control patients with a histologically normal duodenum and a negative AEA. The 2-kb coding region of tTG was amplified in overlapping fragments by reverse transcription polymerase chain reaction (PCR), using five sets of PCR primers. Each overlapping PCR fragment was sequenced using the fmol DNA sequencing system.

RESULTS

tTG transcripts were detected in all samples. There was no difference in the coding sequence of tTG between the four control and eight coeliac patients, even though we observed differences in sequence between our study and the original published sequence. These differences have also been reported in sequences published subsequent to the original description.

CONCLUSIONS

Polymorphisms in the tTG gene have not been observed in coeliac disease patients and therefore cannot explain the creation of neoepitopes.

Calculation of electromagnetic properties of regular and random arrays of metallic and dielectric cylinders

A method is developed to calculate electromagnetic properties of arrays of metallic and dielectric cylinders. It incorporates and exploits cylindrical boundary conditions and Rayleigh identities for efficient, high-accuracy calculation of scattering off individual layers that are stacked into arrays using scattering matrices. The method enables absorption, dispersion, and randomness to be incorporated efficiently, and reproduces known results with vastly improved speed and accuracy. It is used to demonstrate existence of states introduced into photonic band gaps of a dielectric array by disorder, and anomalous absorption behavior in arrays of aluminum cylinders.